The thermal timescale to heat a layer of thickness \(\Delta p\)  is given by \(\tau _{\rm th}=(\Delta p)^2 / K\) , where \(K=\kappa /(\rho c_p)\)  is the thermal diffusivity (in m\(^2\) /s), which we will assume to be of order \(10^{-10}\)  for comet-like objects [1]}, with \(\rho \)  the planetesimal bulk density in kg/m\(^3\) , \(c_p\)  its specific heat in J/kg/K and \(\kappa \)  its thermal conductivity in J/m/s/K. We note that the thermal diffusivity is smaller for cometary material compared to solid amorphous water ice because cometary material is a porous mixture of ices and refractories including organics. The effects of porosity on the actual effective thermal conductivity (hence diffusivity) are consequential [2]}, [3]}. This value is consistent with current measurements of the thermal inertia at the surface of comets [4]}. We calculate that during the Solar System lifetime, i.e. \(t_S=4.6\)  Gyr, the depth to which planetesimals can heat up to the equilibrium temperature of \(\sim \) 40 K [5]} is \(\sqrt{t_S K} \sim 3.8\)  km. After 4.6 Gyr, the layers deeper than 4 km should still retain their primordial temperature of 10-20 K [6]}, [5]} and planetesimals smaller than about 4 km should have no further gas to release as any primordial CO would have already been lost.
